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模式识别中的支持向量机(SVM)教程.pdf

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,,1–43() cKluwerAcademicPublishers,Boston.ManufacturedinTheNetherlands. ATutorialonSupportVectorMachinesforPattern Recognition CHRISTOPHERJ.C.BURGESburges@lucent.com BellLaboratories,LucentTechnologies Abstract.ThetutorialstartswithanoverviewoftheconceptsofVCdimensionandstructuralrisk minimization.WethendescribelinearSupportVectorMachines(SVMs)forseparableandnon-separable data,workingthroughanon-trivialexampleindetail.Wedescribeamechanicalanalogy,anddiscuss whenSVMsolutionsareuniqueandwhentheyareglobal.Wedescribehowsupportvectortrainingcan bepracticallyimplemented,anddiscussindetailthekernelmappingtechniquewhichisusedtoconstruct SVMsolutionswhicharenonlinearinthedata.WeshowhowSupportVectormachinescanhaveverylarge (eveninfinite)VCdimensionbycomputingtheVCdimensionforhomogeneouspolynomialandGaussian radialbasisfunctionkernels.WhileveryhighVCdimensionwouldnormallybodeillforgeneralization performance,andwhileatpresentthereexistsnotheorywhichshowsthatgoodgeneralizationperformance isguaranteedforSVMs,thereareseveralargumentswhichsupporttheobservedhighaccuracyofSVMs, whichwereview.Resultsofsomeexperimentswhichwereinspiredbytheseargumentsarealsopresented. Wegivenumerousexamplesandproofsofmostofthekeytheorems.Thereisnewmaterial,andIhopethat thereaderwillfindthatevenoldmaterialiscastinafreshlight. Keywords:SupportVectorMachines,StatisticalLearningTheory,VCDimension,PatternRecognition Appearedin:DataMiningandKnowledgeDiscovery2,121-167,1998 1.Introduction Thepurposeofthispaperistoprovideanintroductoryyetextensivetutorialonthebasic ideasbehindSupportVectorMachines(SVMs).Thebooks(Vapnik,1995;Vapnik,1998) containexcellentdescriptionsofSVMs,buttheyleaveroomforanaccountwhosepurpose fromthestartistoteach.Althoughthesubjectcanbesaidtohavestartedinthelate seventies(Vapnik,1979),itisonlynowreceivingincreasingattention,andsothetime appearssuitableforanintroductoryreview.Thetutorialdwellsentirelyonthepattern recognitionproblem.Manyoftheideastherecarrydirectlyovertothecasesofregres